Kygios had to come from three games down in the first and third sets, but showed his growing maturity as he calmly worked his way past world number 25 Querrey.
"They have had so much success down the years", said Djokovic.
After the match, Kyrgios was thrilled, and said that it was good to even the score against his American rival who has beaten him twice before in the past.
Hewitt was delighted by the performances of his two singles stars, but wasn't ready to start thinking of a potential semi-final against either 2015 finalists Belgium or Italy.
"(I tried to) play within myself, not try to hit it too big, because that is not really my style".
American captain Jim Courier had said publicly all week that he respected the tenacity and fitness of Thompson, especially in a competition with the Davis Cup's capacity for upsets.
With Australia 2-1 up going into the final day, Kyrgios won 7-6 (7-4), 6-3, 6-4 to give the hosts an unassailable lead in Brisbane.
Kyrgios, enjoying arguably the best run of form of his career so far, showed impressive patience to nullify the big serve of John Isner and win their singles rubber 7-5, 7-6 (7-5), 7-6 (7-5).
Kyrgios, who has polarised Australian tennis lovers, rode a wave of noisy support from a home crowd who were chanting his surname after pulling off a 7-6 (7-4), 6-3, 6-4 win over American substitute Sam Querrey. The British player, drafted into the singles line-up after the injury-enforced withdrawal of world number one Andy Murray, was made to pay for letting slip a 5/2 lead in the second-set tiebreak. "He is a proven player and I knew it was going to be tough", Kyrgios said.
Thompson explained how he broke down Sock's game.
The US kept their hopes of turning the contest around yesterday as they emerged victorious in the doubles rubber to cut the deficit to 2-1 at the Pat Rafter Arena in Brisbane.
A rejuvenated Sock then partnered Steve Johnson to defeat Groth and John Peers in a five set Saturday doubles thriller.
But he jogged to his chair with an uncustomary wide, mid-match smile when he took the second set with a drop shot.
Australia surged back into contention after a Groth forehand down the line secured the crucial break in the fourth set.
AMERICAN Jack Sock has redeemed himself to take the Davis Cup quarter-final against Australia into a deciding day after making good in his late substitution into the doubles.
Trump's US$107m donations record
Unlike Trump, the 2009 committee did not accept corporate contributions and limited individual donations to a maximum of $50,000. Sheldon Adelson attending the fourth Annual Champions Of Jewish Values International Awards Gala in New York City, May 5, 2016.